Equidistance traversal

eqdist1.cpp

#include <algorithm>
#include <vector>
#include <iostream>
#include <iomanip>
#include <fstream>

using namespace std;

struct Point {
    Point(int x, int y) : x(x), y(y), sqDist(x * x + y * y) {}
    bool operator<(const Point& rhs) const { return sqDist < rhs.sqDist; }
    int x, y, sqDist;
};

int main() {
    const int r = 5;
    const int size = r * 2 + 1;

    vector<Point> points;

    for (int y = -r; y <= r; y++)
        for (int x = -r; x <= r; x++) {
            Point p(x, y);
            if (p.sqDist <= r * r)
                points.push_back(p);
        }

    sort(points.begin(), points.end());

    const Point* last = 0;
    for (auto const& p : points) {
        if (last) {
            if (p.sqDist == last->sqDist)
                cout << ", ";
            else
                cout << endl;
        }
        cout << "(" << p.x << "," << p.y << ")";
        last = &p;
    }

    cout << endl << endl;

    std::vector<int> image(size * size, -1);
    last = 0;
    int level = 0;
    for (auto const& p : points) {
        if (last && p.sqDist != last->sqDist)
            level++;
        image[(p.y + r) * size + p.x + r] = level;
        last = &p;
    }
    for (int y = 0; y < size; y++) {
        for (int x = 0; x < size; x++)
            if (image[y * size + x] == -1)
                cout << "  ";
            else
                cout << setw(2) << image[y * size + x];
        cout << endl;
    }
}

eqdist1_output.txt

(0,0)
(1,0), (0,1), (0,-1), (-1,0)
(1,-1), (-1,-1), (-1,1), (1,1)
(2,0), (0,2), (-2,0), (0,-2)
(1,2), (-1,2), (1,-2), (-2,1), (-2,-1), (2,-1), (2,1), (-1,-2)
(2,2), (-2,2), (-2,-2), (2,-2)
(0,3), (-3,0), (0,-3), (3,0)
(1,3), (-1,3), (3,1), (-3,1), (-3,-1), (1,-3), (-1,-3), (3,-1)
(2,-3), (-3,-2), (3,-2), (-2,-3), (-3,2), (3,2), (-2,3), (2,3)
(0,-4), (-4,0), (4,0), (0,4)
(-4,1), (-4,-1), (4,1), (1,-4), (4,-1), (-1,-4), (-1,4), (1,4)
(3,-3), (-3,-3), (-3,3), (3,3)
(4,2), (4,-2), (-4,-2), (2,-4), (-4,2), (-2,-4), (-2,4), (2,4)
(-3,-4), (-5,0), (5,0), (4,3), (-3,4), (-4,3), (0,-5), (4,-3), (-4,-3), (3,-4), (3,4), (0,5)

          13
    131210 9101213
  1311 8 7 6 7 81113
  12 8 5 4 3 4 5 812
  10 7 4 2 1 2 4 710
13 9 6 3 1 0 1 3 6 913
  10 7 4 2 1 2 4 710
  12 8 5 4 3 4 5 812
  1311 8 7 6 7 81113
    131210 9101213
          13